The pion-nucleon σ term from pionic atoms

Abstract

Earlier work suggested that the in-medium πN threshold isovector amplitude b 1 (ρ) gets renormalized in pionic atoms by ∼ 30% away from its ρ = 0 freespace value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate <qq > and the pion decay constant f π in terms of the pion-nucleon σ term σ πN . Accepting the validity of this approach, we extracted σ πN from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value σ πN = 57 ± 7 MeV is robust with respect to variation of πN interaction terms other than the isovector s-wave term with which σ πN was associated. Higher order corrections to the leading order in density involve some cancellations, suggesting thereby only a few percent overall systematic uncertainty. The value of σ πN derived here agrees with values obtained in several recent studies based on near-threshold πN phenomenology, but sharply disagrees with values obtained in recent direct lattice QCD calculations.

Report on scipost_201911_00039v1

“…10 we compare lattice QCD and phenomenological results on σ πN and σ s . The smaller value predicted by lattice QCD is in agreement with the original analysis that yielded σ πN ∼ 45 MeV [15] but it is in tension with recent analyses that yield larger values, such as an analysis based on the Roy-Steiner equations and experimental data on pionic atoms yielding a value of 59.1(3.5) MeV [16] that was confirmed using a large-scale fit of pionic-atom level shift and width data across the periodic table [17] as well as πN scattering lengths from the low-energy data base [18]. Given the significant progress in the determination of σ πN both using experimental data [19][20][21] and lattice QCD this persisting tension needs to be further examined.…”

Nucleon axial, tensor, and scalar charges and σ -terms in lattice QCD

“…We note that the results by RQCD and χQCD after chiral and continuum extrapolation agree with their corresponding value obtained using their physical point ensemble and are thus not included. We include a range of phenomenological results that do not use lattice QCD input [76,77,79,[90][91][92][93] (open circles). phenomenological results limiting ourselves to those that have not used input from lattice QCD.…”

Recent progress on the study of nucleon structure from lattice QCD and future perspectives

“…These include an analysis based on the Roy-Steiner equations and experimental data on pionic atoms yielding a value of 59.1(3.5) MeV [16]. This larger value was confirmed using a large-scale fit of pionic-atom level shift and width data across the periodic table [17] as well as πN scattering lengths from the low-energy data base [18]. Given the significant progress in the determination of σ πN both using experimental data [19][20][21] Figure 9: We show the intrinsic quark spin 1 2 ∆Σ q for the u (upper), the d (center) and s quarks (lower) as a function of the pion mass.…”